Exponentially Closed Fields and the Conjecture on Intersections with Tori

Jonathan Kirby, Boris Zilber

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
13 Downloads (Pure)

Abstract

We give an axiomatization of the class ECF of exponentially closed fields, which includes the pseudo-exponential fields previously introduced by the second author, and show that it is superstable over its interpretation of arithmetic. Furthermore, ECF is exactly the elementary class of the pseudo-exponential fields if and only if the diophantine conjecture CIT on atypical intersections of tori with subvarieties is true.
Original languageEnglish
Pages (from-to)1680-1706
Number of pages27
JournalAnnals of Pure and Applied Logic
Volume165
Issue number11
Early online date9 Jul 2014
DOIs
Publication statusPublished - Nov 2014

Keywords

  • math.LO
  • 03C65, 11G35
  • Exponential fields
  • Anomalous intersections
  • Schanuel's conjecture
  • Predimension

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